5008
GEORGE G. KOERBER AND THOMAS DE VRIES
is more limited than the range of the D.M.E. because of the greater sensitivity of the former electrode. For example, the reduction of 0.1 111 potassium ion a t the R.M.E. would be expected to begin at a potential about 140 mv. less negative than the potential of the same reduction a t the D.M.E. because the K.iI1.E. is 200 times more sensitive than the D.M.E. Likewise, the anodic dissolution of mercury a t the R.M.E. would occur a t a more negative potential than a t the D.M.E. The range of potentials of the R.M E. would therefore be expected to be less by several tenths of a volt. In practice it was found that the range was even more restricted, arid that the residual current became large, presumably due to the reduction of water, a t potentials more negative than -1.2 v. vs. S.C.E. unless (1) the surface of the groove of the electrode was highly polished, and ( 2 ) vibration of the electrode was minimized. In addition i t was found that the range B was increased if the chemical and physical nature of the surface of the groove was such that the interfacial tension between plastic and mercury was as small as possible and the interfacial tension between plastic and electrolyte was as large as possible. The residual current (Fig. 9) of the R.M.E., a t its present stage of development] is such that
[CONTRIBUTION FROM
THE
VOl. 74
analysis for the alkaline earth ions and the alkali ions is not possible.” Aluminum ion can be reduced but the analysis for aluminum a t low concentrations is not practical. Most of the other metal ions that can be determined with the D.M.E. can probably be determined with the R.M.E., although this expectation has not yet been put to an exhaustive test. Application~.~-The current-voltage curves of the K.M.E. can be used for the qualitative and quantitative analysis of electro-reducible substances a t concentrations as low as lo-’ M . Metal M can ions a t concentrations down to 5 X be determined by a combination of coulometric and voltarnnietric techniques. The R.M.E. is also useful for amperometric titrations and “derivative” analysis.18 Acknowledgment.-The author is indebted to Professor I. M. Kolthoff, University of Minnesota, for interesting discussions and valuable suggestions. Part of this study was aided by a grant from the Shell Oil Company. (17) The surface of the groove of the R.M.E. of Fig. 9 was coated with a thin layer of “Lubriseal,” a high molecular weight saturated hydrocarbon. See reference 3. (18) 0 H Muller, ref. l e , p 132
CHICAGO 37, ILLINOIS
DEPARTMENT OF CHEMISTRY, PURDUE UNIVERSITY 1
Electrode Potentials in Liquid Hydrogen Fluoride BY GEORGEG. KOERBER’ AND THOMAS DE VRIES RECEIVED M A Y22, 1952 The values of the electromotive force of cells of the type M,MFt(s)/HF(NaF)/HgaF*(s)/Hg where M represents cadmium, copper or lead were found a t 10 and 0’. These were used to evaluate the standard free energies of formation of mercurous, cupric and lead fluorides. A study of the vapor pressures of the systems mercurous fluoride-hydrogen fluoride, cadmium fluoride-hydrogen fluoride, and lead fluoride-hydrogen fluoride was made a t 0’. Lead fluoride was found to form an addition compound with hydrogen fluoride with the formula P ~ F Y ~ ~ / ~The H Fcell . Hg,HgzFz(s)/NaF(in HF)//NaF,H80F,AgF (in HF)/Ag was studied a t 0’ over a range of concentrations of the electrolytes. The data fron this were used t o calculate activity coefficients of silver fluoride in liquid hydrogen fluoride. An ion size parameter of 1.9 A. was found for silver fluoride in the solutions studied. The standard free energy of formation of AgF.HF from silver, fluorine and hydrogen fluoride was calculated.
It has been known for a long time that liquid hydrogen fluoride is a good ionizing solvent medium. With the exception of the work by 0. T. KrefftB2 who evaluated the standard free energy of formation of liquid hydrogen fluoride a t 0’ by measuring the potential of the cell H2(Pt)/”F(KF)/F2(Pt), the use of electrode potentials in liquid hydrogen fluoride as a means of studying the thermodynamics of solutions in hydrogen fluoride, and of evaluating thermodynamic properties of metal fluorides has been neglected. In this research] cells of the type M,MFz(s)/ HF(NaF)/HgZFz(s),Hg where M represents cadmium, copper and lead, were measured in order to evaluate the standard free energies of formation of the metal fluorides and the cell Hg,HgzFz(s)/ NaF(in HF)//NaF,HSOF,AgF(in HF)/Ag was stud(1) Abstract from the P h D. dissertation of George G. Koerber whose present address is Bell Telephone Laboratories, M u r r a y Hill, New Jersey. (2) 0.T. Krefft,”Inaug. Diss.,”GreifswaldInstitut fur Physikdlische Chemie, Greifswald, Germany, 1939.
ied in order to investigate the thermodynamics of solutions in hydrogen fluoride. Vapor pressure measurements were made of the systems metal fluoride-hydrogen fluoride in order to determine whether any of the metal fluorides formed addition compounds with hydrogen fluoride. Experimental Materials.-Harshaw “Anhydrous” hydrogen fluoride of a purity of 99.5% was used directly from the cylinder. The water content of this material was less than 0.2%. Lead, cadmium and mercurous fluorides were prepared by treating the carbonates with hydrofluoric acid, Baker Reagent Grade. Cupric fluoride was prepared by passing hydrogen fluoride over the basic carbonate a t 200”. Copper and cadmium amalgams were prepared by electrolysis and lead amalgam was prepared by mixing the proper proportions of spectroscopically pure lead and triple distilled mercury. Two-phase amalgams were used throughout this research. Silver oxide was prepared by precipitation of the oxide from a solution of silver nitrate with potassium hydroxide. Silver and lead stick electrodes were made by inserting silver wire or lead sticks into Teflon plugs that screwed into the base of the cell. These were made reversible by etching
ELECTRODE POTENTIALS IN LIQUID HYDROGEN FLUORIDE
Oct. 20, 1952
Ii
5009
n
B
Fig. 1.-Diagram
of cell: A, lead wires; B, liquid hydro-
gen fluoride; C, paraffin; D, liquid junction capillary; E,
silver electrode; F, mercurous fluoride; G, mercury. the electrode under a mixture of the metal nitrate and nitric acid. Apparatus and Procedures.-The cell design is shown in Fig. 1. The hollow tube connecting the two arms of the cell was replaced with a solid Teflon tube with a pin-hole through it for the cell Hg,HgzFz(s)/NaF(in HF)//NaF, HaOF,AgF(in HF)/Ag. The liquid junction was formed in the pin-hole. The thermost$ was the conventional water-bath type Potentials were measured with a Leeds controlled to 0.1 and Northrup Student Potentiometer calibrated with an Eppley Standard Cell. Solutions of a solute in hydrogen fluoride were prepared by condensing hydrogen fluoride into a weighed Teflon bottle to which the desired amount of solute was then added. The cell Hg,HgzFz(s)/NaF( in HF)//NaF,H$OF,AgF( in HF)/Ag had solutions of equal ionic strength on each side of the liquid junction. The solution in contact with the silver electrode was made by adding a mixture of silver oxide and sodium fluoride t o hydrogen fluoride. The proportions of sodium fluoride and silver fluoride in the mixture were such that the concentration of the silver fluoride in the resulting solution was equal to '/la of the total concentration of all the electrolytes. Water dissolved in hydrogen fluoride is a strong electrolyte ionizing t o form HaO+ and F- ions.* Solutions and the cell were placed separately in the thermostat for an hour prior to filling the cell in order that the cell would reach equilibrium before the liquid junction lost its spherical symmetry. Vapor pressure measurements of the systems metal fluoride-hydrogen fluoride were made by use of the apparatus shown in Fig. 2. Measurements were made a t 0'. The calculations were based upon the weight of hydrogen fluoride absorbed in an absorption tube through which a certain volume of air saturated with hydrogen fluoride had been passed. The air saturated with hydrogen fluoride was displaced from the apparatus by introducing a measured volume of mercury into the apparatus. The molecular weight of the hydrogen fluoride in the vapor phase was assigned the value 92.4 by interpolating the results of vapor density measurements made by Simons and Hildebrand.'
.
Experimental Results Vapor Pressure Measurements of the Systems Metal Fluoride-Hydrogen Fluoride.-Lead fluoride was found to form an additional compound with (3) K.Fredenhagen, G.Cadenbach and W. Klatt, 2. physik. Chcm., A164, 176 (1933). (4) J. H. Simons and J. H. Hildebrand, THISJOURNAL, 46, 2188 (1924).
Fig. 2.-Vapor pressure apparatus: A, buret; B, clamp; C, adsorption tube; D, broken pellets of sodium hydroxide.
hydrogen fluoride under the experimental conditions (see Table I). The formula of the compound is PbFr2l/zHF and the vapor pressure of the system PbFt-PbFz.21/zHF was found to be 0.014 atmosphere. From this the free energy change for the reaction PbFz(s)
+ 2l/*HF(l) +P ~ F Z . ~ ~ / ~ H F ( S )
was computed to be -4.5 kcal. a t 0'. TABLE I THEVARIATION OF VAPORPRESSURE OVER MIXTURESOF H F AND PbFz WITH CHANGES IN THE RATIOOF H F TO PbF? Ratio of moles H F to moles PbFt
Vapor pressure, atm.
0.6 1.40
0.047 .013 .Ol5 .467 .447 .495
2.49 2.71 3.43 Pure H F
No evidence was found for the existence of an addition compound between cadmium or mercurous fluorides and hydrogen fluoride. The Cell Pb(het. amal.), PbF2.21/2HF(s)/HF (NaF)/HgzFz(s) ,Hg.-For this cell the reaction is
+
+
Pb(het. amal.) 2l/zHF(1) HgZFz(s) +P ~ F z . ~ ~ / z H F 4- 2Hg(l); E213 = 1.0637 dz 0.0008 volt, AF273 = -49.09 kcal.
From Gerke's6 value of the potential of the cell Pb (het . amal.) /Pb ++/Pb (s), the following free energy change is calculated Pb(s)
+Pb(het. amal.), L i F 2 7 3
(5) R. H. Gerke, ibid., 44, 1684 (1922).
= -0.20 kcal.
GEORGE G. KOERRER AND THOMAS DE VRIES
5010
Combination of these results yields
+ 2’/21HF(l) + Hg*FZ(S) --+
+
PhFz,2*/2HF(s) 2Hg(l); AF273 = -49.09 ked. (1)
I’h(s)
The Cell Cu(het. amal.),CuFz(s)/HF(KaF)/ HgzFz(s),Hg.-For this cell the reaction is
+
+
Cu(het. amal.) Hg2F2(s) --+ CuF*(s) 2Hg(l); E283 = 0.283 i 0.002 volt, AF233 = -13.1 kcal. E273 = 0.274 f 0.005 volt, AF2,3 = -12.6 kcal.
Vol. 74
obtained for the standard free energy of formation of cadmium fluoride Cd(s)
+
Fz(g)
--+
CdFz(s);-
AFo283
AFOS,~= -1d.8 kcal.
= -154.5
kcal.,
Equations (4) and ( 5 ) can be combined with the appropriate value of the standard free energy of formation of cadmium fluoride to give
The following values are obtained from Oku’s6 nieasurements of the cell Cu/Cu++fCu(het. anial.) Equation (7) can be combined with the result from Cu(s) --+ Cu(het. anial.); A F s 3 = -0.19 kcal., A F v ~ = the measurement of the vapor pressure of the -- 0 . I6 kcal. system lead fluoride-hydrogen fluoride Combination of these results yields I’bFz(5) + Z’/iHF(I) +PbFz,2’/2HF(s); AI7273 = -4 5 CU(S)
+ Hg,Ff(s) +C U F ~ ( S+) 2Hg(l); kcal. ( 2 ) ;
AF273 =
AFisj
-12.8 kcal.
-13.2 (3
The Cell Cd(het. anial.), CdF2(s)/HF(NaF)/ HgzFz(s),Hg.-The cell reaction is
+
+
Cd(het. amal.) HgpFz(s) -+ CdFa(s) 2Hg(l); Ensa = 1.0337 f 0.0009 volt, AF283 -44.70 kcal.
Measurements of the cell Cd/Cd++/Cd(het. ar11al.j’ yields Ccl(s)
+Cd(het. amal.); AF?Jz
= -2.45 kcal.
kcal
.
to give Pb(s)
+ F2(g) + PhFp(s);
A.FOar3 = -149.3
kcnl. (8)
Combination of equations (1) and (7) gives 2Hg(l)
+ Fa(g) --+ HgpF*(s);
AF“273
= -104.5
k d . (9)
Combination of equations ( 2 ) and (6) and (3) and (Oj gives Cu(s)
+
FZ(g)
+ CuF,(s); AF283
AF273
=
-117.3
kcal.,
= -117.7 kcal.
Combining these results yields
Extrapolation of Jahn-Held and Jellinek’s* data for the standard free energy of formation of kcal. (4) lead fluoride gives a value of - 148.0 a t 0’ as comThe Cell Pb(het. amal.), PbF2.21/2HF/HF- pared with - 149.1 kcal. from this research. About (NaF)/CdFs(s),Cd(het. amal.).-For this cell the 0.2 kcal. of this discrepancy may be ascribed to an reaction is uncertainty in the value found for the vapor Pb(het. amal.) + CdF?(s) + 2l/2HF(l) --+ P b F ~ . 2 ~ / 2pressure of the system pbF~-PbF2.2l/~HF. An independent check can be made upon the HIT f Cd(het. amal.); = 0.0300 + 0.0012 volt, AF273 = -1.38 kcd. value found for the standard free energy of formation of cupric fluoride in the following way. The Combination of this result with entropies of copper and fluorine a t 25’ are 7.96 Cd -+ Cd(het. ainal.); AF273 = -2.61 kcal.7 and 48.6 E.U.9 and the entropy of cupric fluoride a t PI, +Ph(het. a n i a l . ) ; AF?73 = -0.19 kca1.j 2.5” can be calculated by the method of Latimerlo to be 25.7 E.U. From this the entropy change for gives Fz(g) + CuFz(s) is calculated C ~ ( S )+ PbFr,2’/2HF(s) --f CdF2(s) + PI) + 2’/?HF; the reaction Cu(s) to be -31.5 E.U. From reference (8) i t is found AF2;a = -1.04 kcal. (5) All of the above cells were measured over a range that the enthalpy change for the reaction is - 126.9 of mole fractions of sodium fluoride of 0.01 to 0.04. kcal. Combining these gives a value of -117.5 Cells containing the Pb(het. amal.), PbFz*2l/zHF kcal. a t 298°K. for the calculated standard free electrode would be expected to have potentials energy of formation of cupric fluoride. This comthat would be dependent upon the activity of the pares well with the value found in this research. There is not sufficient thermal data in the literahydrogen fluoride. If i t be assumed that the acture to make an independent check of the value tivity of the hydrogen fluoride is equal to its mole found for mercurous fluoride. fraction, the variation of potential with mole fracThe Cell Hg,HgzFz(s)/NaF(in HF)//NaF,H30F, tion can be calculated froni the equation AgF(in HF)/Ag.-This cell was studied for the 5 x 0.0812 purpose of investigating the thermodynamics of E = EO + - . - 4 - - log ‘Yep. solutions in hydrogen fluoride. The liquid junction The extreme variation of potential with concentra- potential was minimized by making the ionic tion would be 0.0012 volt, which is so near to the strengths of the solutions on both sides of the standard deviation of the measurements that no junction equal and by having the mole fraction of definite change with concentration could be ob- silver fluoride low in comparison with the mole fraction of the sodium fluoride. The mole fraction served. Jahn-Held and Jellineks evaluated the standard of silver fluoride was equal to 2/13 of the total mole free energy of formation for a number of metal fraction of all the electrolytes in the solution in fluorides a t 15, 25 and 35”. The following results contact with the silver electrode. The potential are obtained by extrapolation of the values they of the cell was measured over a range of ionic (e) &I. Oktr, Science Ripouts Tohokir I m p . U n i v . Ser. I , 22, 290 strengths from 0.5005 to 2.503. The cell reaction Ctl!~)
+ Hg?Fl(s)+CdFt(s) + 2Hg(l);
AF283
= -50.51
+
11 933).
(7) “International Critical Tables,” Vol. V I I , p. 250, 1930. ( 5 ) W. Jahn-Held and K. Jelliriek, Z. Elekfrochem., 42, 401 1193G).
(9) National Bureau of Standards, “Selected Values of Chemical Thermodynamic Properties.” Table 34 (1949). (10) W. M I,atimer, THISJ O U R N A L , 43, 818 (1921).
Oct. 20, 1952
ELECTRODE POTENTIALS I N LIQUID HYDROGEN FLUORIDE
+
+
+
is Hg Agf F'/zHgzFz(s) Ag, and the equation relating the potential of the cell to the concentration of the ions to which the electrodes are reversible is E = Eo + 0.542 log XAg+ x fAp'XF- x fF- (10) If the assumption is made that the individual ion activity coefficients of the silver and fluoride ions depend only upon the ionic strength, and not upon the ion species making up the ionic strength, the Debye-Huckel equation can be substituted into equation (IO) to give E = Eo + 0.0542 {log X k + X X F f 2Cp) +
(11)
Since the mole fraction of the silver ion is equal to of the mole fraction of the fluoride ion, this can be substituted into equation (11) and the result rewritten as EO'
=E
- 0.0542
i
log -- :2
-2A4iI
=
Eo +
0.1084C~ (12)
The constant A has the value 0.529 for hydrogen fluoride a t 0'. All of the quantities on the lefthand side of equation (12) are known or measured. The left-hand side of equation (12) is designated as EO'. The various values of Eo' found for different ionic strengths are given in Table 11. Figure 3 shows a plot of Eo' against the ionic strength. The intercept gives the Eo of the cell, which is 0.3510 volt, and the slope of the line gives a value of 0.0793 for the parameter C. The data in Table I1 marked with an asterisk were obtained by a slightly different procedure. In these cases the concentration of sodium fluoride was constant throughout the cell and silver fluoride was added to the solution placed in contact with the silver electrode. In these cases it can be shown that E - 0.0542 (log X N ~ xF XAgF - A ( d M d p ' ) 1 = Eo f
0.3700
L
5011
I
0.3500 1.o 2.0 Ionic strength. ' . Fig. 3.-E"' us. ionic strength a t 0
3.0
posed to represent the mean ionic diameter. This method of calculating a gives i t the value 1.9 X cm., which is comparable to similar values found for electrolytes in aqueous solutions. TABLE I11 CALCULATED ACTIVITY COEFFICIENTS O F SILVER FLUORIDE IN HYDROGEN FLUORIDE AT 0" Mole fraction AgF
Activity coefficient
0.001 .01 * 02 .03 .04 .05(satd.)
0.752 .460 ,352 .293 .254 .229
The solubility of silver fluoride in hydrogen fluoride was found by Fredenhagen and co-workers3 to be 33 g. per 100 g. of hydrogen fluoride a t - 15'. The compound AgFaHF is probably the solid phase in contact with the saturated solution a t O'." If it be assumed that the solubility does not change 0.0542C(p + M ' ) greatly with temperature, the standard free energy The left-hand side of this equation serves as the of formation of AgF.HF can be calculated approxidefinition of the Eo' that appears in Table I1 for mately from the results of this research. The the data t o which i t is applicable. mole fraction of silver fluoride in its saturated soluTABLE I1 tion is 0.0494. The activity coefficient of silver fluoride a t this concentration is 0.227. These VARIATION OF THE POTENTIAL OF THE CELLHg,HgzFz(s)/ NaF( IN HF)//NaF,H,OF,AgF(IN HF)/Ag WITH CON- values can be substituted into equation (10) to calculate the potential of the hypothetical cell CENTRATION OF ELECTROLYTES AT 0' Hg,HgzFz(s)/NaF.(a L: 0.227 X O.O494)//AgF Ionic strength Mole fraction EO' Nap AgF Potential P P' (satd.)/Ag. This calculation gives a value of 0.1400 0.05000 0.00769 0.0964 2.503 2.503 0.3721 volt which corresponds to a free energy change of .04000 .00615 .0915 2.002 2.002 .3682 -3.23 kcal. for the reaction Hg(1) AgF (satd. .03600" ,0060 ,0901 1.802 1.502 ,3666 soln.) + '/zHgzFz(s) Ag(s). This can be com.03400" .0040 .0763 1.702 1.502 .3613 bined with the value of the standard free energy ,03200" .0020 .0642 1.602 1.502 ,3644 of formation of mercurous fluoride to give
+
+
+
.02000 .00308 .0737 1.001 1.001 .3593 .01000 ,00154 .0543 0.5005 0.5005 ,3557 0 A slightly different procedure was used for these data. Eo' is given by the formula Eo' = E - 0.0542j log X b X X r - A(fi fi')l.
+
Table I11 is a list of calculated activity coefficients for silver fluoride in hydrogen fluoride a t 0'. These coefficients were calculated from the Debye-Huckel equation - A V'G logf, = ~I
+ aBp
in order to evaluate the quantity a which is sup-
Ads)
+
'/zFz(g)
+ HF(1) AgF.HF(s); -49.0 kcal . --f
.IFm =
Acknowledgment.-The authors wish to express their gratitude to the Allied Chemical and Dye Corp. for providing the funds for the fellowship under which part of this work was done, and to Dr. A. L. Rocklin of the Dow Chemical Co., Pittsburg, Calif., who directed the research during its initial phases. LAFAYETTE. INDIANA (1 1) J. H. Simons, E d . , "Fluoriiie Chemistry," Academic Publishing C o . , Inc., New York, N. Y., 1949.
